Review for Exam 2 SHORT ANSWER. Write the word or phrase that
Review for Exam 2
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the equation.
3x
4
12
=
1)
x-3 x
2
x - 3x
1)
2)
3x + 10 = 5 - 2x
2)
3)
10 + x +
3)
4)
5)
3
3
11 - 5x = -1
6x - 3 + 7 = 5
4x2 - 6x - 2 =
4)
3
4x2 + 8x + 9
5)
6) (x + 2)2/3 - 3(x + 2)1/3 - 10 = 0
6)
7) x4 + 720 = 89x2
7)
8) 42x-2 - 1x-1 = 56
8)
For the points P and Q, find the coordinates of the midpoint of the segment PQ.
9) P(9 5, - 10), Q(- 5, 0)
9)
Determine whether the three points are the vertices of a right triangle.
10) (-11, 6), (0, -5), (2, -3)
10)
Determine whether the three points are collinear.
11) (-1, -3), (1, 1), (9, 17)
11)
Find the center-radius form of the equation of the circle.
12) center (-9, -8), radius 14
12)
Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
13) x2 + y2 + 8x - 10y + 41 = 0
13)
Find the center and radius of the circle.
14) x2 + y2 - 8x - 10y + 16 = 0
14)
1
Decide whether the relation defines a function and find the domain and range
15)
16)
15)
16)
Decide whether the relation defines a function.
17) y2 = 5x
17)
Determine the intervals of the domain for which the function is increasing, decreasing, and constant.
18)
18)
Graph the line and give the domain and the range.
19) -2x + 16 = 0
19)
2
Graph the line described.
20) through (-3, -9); m = 4
20)
Find the average rate of change illustrated in the graph.
21)
21)
Value of
Car (in
thousands
of dollars)
Year
Write an equation for the line described. Give your answer in slope-intercept form.
22) through (2, 8) and (0, -7)
22)
Write an equation for the line described. Write the equation in the form specified.
23) perpendicular to -5x + y = 5, through (5, 5); slope-intercept form
23)
24) parallel to 9x + 7y = -45; through (2, -5); standard form
Solve the problem. Write all linear equations in slope-intercept form.
25) A company can make 12 airplane engines for $74,000, while 19 airplane engines cost
$77,500. Find a linear equation that models the cost to produce x airplane engines.
3
24)
25)
Graph the function.
3x2 ,
if x -1
26) f(x) = 3,
if -1 < x < 1
3x + 1, if x 1
26)
Give a rule for the piecewise-defined function. Then give the domain and range.
27)
27)
Graph the function.
28) g(x) = - x + 2 - 2
28)
4
29) g(x) =
1
x+5 +6
4
29)
Determine whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or none of
these.
30) y = -5x3 + 9x
30)
Determine if the function is even, odd, or neither.
31) f(x) = 3x4 - 5x - 8
31)
32) f(x) = x4 - 4x2 + 1
32)
5
Answer Key
Testname: REVIEW FOR EXAM # 2 245
1)
4
3
2)
3
4
3)
4) -
5
6
5) -
11
14
6) {-10, 123}
7) {-4 5, -3, 3, 4 5}
6
7
,8)
7
8
9) 4 5, -
10
2
10) Yes
11) Yes
12) (x + 9)2 + (y + 8)2 = 14
13) no; the graph is the point (-4, 5)
14) center: (4, 5); radius: 5
15) Function
16) Not a function
17) Not a function
18) Increasing [3, ); Decreasing (- , -3]; Constant [-3, 3]
19) D = {8}, R = (- , )
6
Answer Key
Testname: REVIEW FOR EXAM # 2 245
20)
21) -$1000.00 per year
15
x-7
22) y =
2
23) y = -
1
x+6
5
24) 9x + 7y = -17
25) y = 500x + 68,000
26)
27) f(x) = -2x if x 1 ; Domain: (
x + 1 if x > 1
, ), Range: (
, )
7
Answer Key
Testname: REVIEW FOR EXAM # 2 245
28)
29)
30) origin only
31) Neither
32) Even
8
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